Copolymer formulation for directed self-assembly, methods of manufacture thereof and articles comprising the same

ABSTRACT

Disclosed herein is a composition comprising a block copolymer; where the block copolymer comprises a first polymer and a second polymer; where the first polymer and the second polymer of the block copolymer are different from each other and the block copolymer forms a phase separated structure; an additive polymer; where the additive polymer comprises a bottlebrush polymer; and where the bottlebrush polymer comprises a polymer that is chemically and structurally the same as one of the polymers in the block copolymer or where the bottlebrush polymer comprises a polymer that has a preferential interaction with one of the blocks of the block copolymers; and a solvent.

CROSS REFERENCE TO RELATED APPLICATION

This US Non-Provisional application claims the benefit of U.S.Provisional Application Ser. No. 62/121,261, filed 26 Feb. 2015, theentire contents of which are hereby incorporated by reference.

BACKGROUND

This disclosure relates to a copolymer formulation for directedself-assembly, methods of manufacture thereof and to articles comprisingthe same.

Directed self-assembly (DSA) of block copolymers has been identified asa candidate technology to extend the state of current opticallithography. In DSA, small pitch sizes are achieved by directing theself-assembled block copolymer nanodomains to a lithographicallypatterned substrate. One of the leading methods for DSA involves achemical pattern to align a lamellar morphology of a block copolymer,such as polystyrene-block-poly(methyl methacrylate), or PS-b-PMMA. Thepreferred process scheme, shown in FIG. 1, begins by patterning an arrayof sparse guide stripes (e.g., polystyrene (PS) generally manufacturedfrom a crosslinked polystyrene mat. After the stripes are etched (alsotermed “etch trimming”) to the proper dimension, the brush polymer iscoated over the stripes, baked to induce chemical grafting, and thenexcess brush polymer is removed by rinsing with a solvent such aspropylene glycol methyl ether acetate (PGMEA) to leave a relatively flatsubstrate with chemical contrast. The substrate is then treated with ablock copolymer (e.g. poly(styrene-b-methylmethacrylate)), which afterannealing aligns to the substrate to multiply the density of the initialpattern. In this two-step method that involves first applying the brushfollowed by applying the block copolymer (BCP), the composition of thebrush has to be controlled over a fairly tight range in order to achievegood DSA results.

It is therefore desirable to use compositions where the alignmentbetween domains can be easily achieved and where the ranges of thepolymers are not so tightly controlled.

SUMMARY

Disclosed herein is a composition comprising a block copolymer; wherethe block copolymer comprises a first polymer and a second polymer;where the first polymer and the second polymer of the block copolymerare different from each other and the block copolymer forms a phaseseparated structure; an additive polymer; where the additive polymercomprises a bottlebrush polymer; and where the bottlebrush polymercomprises a polymer that is chemically and structurally the same as oneof the polymers in the block copolymer or where the bottlebrush polymercomprises a polymer that has a preferential interaction with one of theblocks of the block copolymers; and a solvent.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic depiction of a prior art method that involvesdomain alignment by first applying the brush followed by applying theblock copolymer;

FIG. 2(A) depicts a substrate with a photoresist having holes ofdiameter d₁ disposed thereon;

FIG. 2(B) depicts the substrate of the FIG. 2(A) with a block copolymerdisposed in the holes;

FIG. 2(C) shows the substrate after etching to remove the cylindricalcore;

FIG. 2(D) depicts a substrate with a photoresist having holes ofdiameter d₁ and holes of diameter d₂ disposed thereon, where d₂ isgreater than d₁;

FIG. 2(E) shows that a continuous cylindrical core in formed in thenarrow diameter hole while discontinuous cylinders (discs) are formed inthe broader diameter hole;

FIG. 2(F) shows that a continuous cylindrical core can be removed viaetching from the narrow diameter hole while only one of the discs can beetched from the broader diameter hole;

FIG. 3(A) is an enlarged depiction of the discontinuous discs present inthe hole having the broader diameter. This is considered a defect;

FIG. 3(B) shows how the defective discontinuous discs can be preventedfrom forming by using a composition that comprises bottlebrush polymers;

FIGS. 4(A) and 4(B) depict ideal and defect morphologies arising fromthe self-assembly of a linear PS-b-PMMA block copolymer in a cylindricalpre-pattern with PS-block-attractive walls, including top-down andcross-section views. PMMA density profiles are shown in light colors;

FIG. 5 is a graph showing defect formation energy versus hole criticaldimensions for a pure diblock copolymer;

FIG. 6 is a graph showing defect formation energy as a function ofbottlebrush loading;

FIG. 7 is a graph showing defect formation energy as a function ofbottlebrush loading;

FIG. 8 is a graph showing a comparison of defect formation energy as afunction of bottlebrush loading for PMMA-BB and PS-BB;

FIG. 9 is a schematic diagram showing ideal and defect morphologiesarising from assembly of a linear AB diblock copolymer in a trenchpre-pattern with A-block-attractive walls, including top-down andcross-section views;

FIG. 10 is a graph showing defect formation energy as a function oftrench width for line/space graphoepitaxy with a linear diblockcopolymer and linear diblock copolymer/bottlebrush polymer blends;

FIG. 11 is a photomicrograph that depicts the morphology for theComparative Examples D, E and F; and

FIG. 12 is a micrograph that depicts the morphology of Examples 17, 18and 19.

DETAILED DESCRIPTION

As used herein, “phase-separate” refers to the propensity of the blocksof block copolymers to form discrete microphase-separated domains, alsoreferred to as “microdomains” or “nanodomains” and also simply as“domains”. The blocks of the same monomer aggregate to form periodicdomains, and the spacing and morphology of domains depends on theinteraction, size, and volume fraction among different blocks in theblock copolymer. Domains of block copolymers can form duringapplication, such as during a spin-casting step, during a heating step,or can be tuned by an annealing step. “Heating”, also referred to hereinas “baking”, is a general process wherein the temperature of thesubstrate and coated layers thereon is raised above ambient temperature.“Annealing” can include thermal annealing, thermal gradient annealing,solvent vapor annealing, or other annealing methods. Thermal annealing,sometimes referred to as “thermal curing” can be a specific bakingprocess for fixing patterns and removing defects in the layer of theblock copolymer assembly, and generally involves heating at elevatedtemperature (e.g., 150° C. to 400° C.), for a prolonged period of time(e.g., several minutes to several days) at or near the end of thefilm-forming process. Annealing, when performed, is used to reduce orremove defects in the layer (referred to as a “film” hereinafter) ofmicrophase-separated domains.

The self-assembling layer comprising a block copolymer having at least afirst polymer derived from polymerization of a first monomer and asecond polymer derived from polymerization of a second monomer thatforms domains through phase separation. “Domain”, as used herein, meansa compact crystalline, semi-crystalline, or amorphous region formed bycorresponding blocks of the block copolymer, where these regions may belamellar, cylindrical, or spherical and are formed orthogonal orperpendicular to the plane of the surface of the substrate.Perpendicularly oriented lamellae provide nanoscale line patterns, whilethere is no nanoscale surface pattern created by parallel orientedlamellae. Where lamellae form parallel to the plane of the substrate,one lamellar phase forms a first layer at the surface of the substrate(in the x-y plane of the substrate), and another lamellar phase forms anoverlying parallel layer on the first layer, so that no lateral patternsof microdomains and no lateral chemical contrast form when viewing thefilm along the perpendicular (z) axis. When lamellae form perpendicularto the surface, the perpendicularly oriented lamellae provide nanoscaleline patterns, whereas cylinders that form perpendicular to the surfaceform nanoscale hole patterns. Therefore, to form a useful pattern,control of the orientation of the self-assembled microdomains in theblock copolymer is desirable. In an embodiment, the domains may have anaverage largest dimension of about 1 to about 25 nanometers (nm),specifically about 5 to about 22 nm, and still more specifically about 7to about 20 nm.

The term “M_(n)” used herein and in the appended claims in reference toa block copolymer of the present invention is the number averagemolecular weight of the block copolymer (in g/mol) determined accordingto the method used herein in the Examples.

The term “Mw” used herein and in the appended claims in reference to ablock copolymer of the present invention is the weight average molecularweight of the block copolymer (in g/mol) determined according to themethod used herein in the Examples.

The term “PDI” or “

” used herein and in the appended claims in reference to a blockcopolymer of the present invention is the polydispersity (also calledpolydispersity index or simply “dispersity”) of the block copolymerdetermined according to the following equation:PDI=M _(w) /M _(n).

The transition term “comprising” is inclusive of the transition terms“consisting of” and “consisting essentially of”.

The term “and/or” is used herein to mean both “and” as well as “or”. Forexample, “A and/or B” is construed to mean A, B or A and B.

The terms “brush” or “brush polymer” as used herein to describe apolymer containing a reactive functional group that is capable ofreacting with a functional group upon the surface of the substrate toform a layer of polymer chains attached to the substrate. The terms“mat” or “mat-like film” are used to describe a polymeric layer on asubstrate formed by disposing a polymer having reactive substituentsalong the chain backbone capable of reacting either with itself or acrosslink-inducing additive to form bonds or crosslinks betweenindividual chains of the polymer after it is disposed upon thesubstrate. A brush polymer is one where the chain backbone is orientedperpendicular to the substrate while a mat polymer is one where thechain backbone is oriented parallel to the substrate. Brush polymersgenerally have a reactive functionality that permit it to be bonded withthe substrate.

A bottlebrush polymer comprises a polymeric chain backbone and haspolymeric arms extending radially from the chain backbone. In otherwords, the bottlebrush polymer comprises a polymeric chain backbone withgraft polymers (the polymeric arms) that are bonded (either covalently,ionically or via hydrogen bonding) with the chain backbone. The graftpolymer (i.e., the arms) may comprise polar polymers, non-polarpolymers, or combinations thereof. For example, a portion of the chainbackbone may have polar polymers grafted onto it, while another portionof the chain backbone may have non-polar polymers grafted onto it. Thepolar polymers and the non-polar polymers may be sequentially arrangedin sections vertically along the chain backbone. In another embodiment,the polar and non-polar polymers may be opposedly arranged on the chainbackbone i.e. they extend out radially in different directions but areinterspersed with each other. In other words, the polar graft polymerextends in a first direction and may be bonded with the polymer chainbackbone between two non-polar graft polymers that are also bonded withthe polymer chain backbone but extend in a second direction. The bottlebrush polymer does not contain any reactive functionalities that permitit to reactively bond with the substrate. Bottle brush polymers are notcovalently, ionically or hydrogen bonded with the substrate.

Disclosed herein is a composition (also referred to herein sometimes asa solution) comprising a block copolymer and an additive polymer thatfacilitates directed self-assembly of the polymer domains. The additivepolymer is a bottlebrush polymer. In an embodiment, the compositioncomprises an intimate mixture of the complete volumes of the blockcopolymer and the additive polymer without either the block copolymerand the additive polymer undergoing phase separation. In other words,the composition comprising the block copolymer and the additive polymeris in the form of a single phase and is homogeneous throughout itsentire volume. In another embodiment, the composition comprises asolvent in addition to the block copolymer and the additive polymer. Thesolvent is compatible with one or both of the block copolymer and theadditive polymer.

In directed self-assembly (DSA), it is desirable to achieve a desiredmorphology that is defect-free and that can be annealed to athermodynamic minimum defect state or to a defect free state within auseful short time. One manner of accomplishing this is by blending a“bottlebrush” polymer with a block copolymer. This combination providesimproved self-assembly of the block copolymer (BCP) because thebottlebrush polymer (BB) acts as a “scaffold” in promotingself-assembly. The shape of the bottlebrush polymer topology and thegeneral stiffness of the chain backbone cause favorable constraints onits placement into a film or into a confined volume such as a trench orin a contact hole. Thus the graft (polymer) arms of the bottlebrushpolymer create regions within the film where it is energeticallyfavorable for compositionally similar or chemically compatible blocks ofthe block copolymer to associate. As a result, the block copolymeraligns with the grafted arms of the bottlebrush polymer. If thebottlebrush polymer is long enough (e.g., has a high enough molecularweight chain backbone), the grafts along the chain backbone will createextended domains of structurally similar polymer units, which will thenscaffold extended association of the similar block of the blockcopolymer. A scaffold is an orientation framework that assists to guideor template the proper position of the majority block copolymer. As afurther result, the block copolymer will be scaffolded into formingextended regions of perfectly aligned self-assembly. If the compositionof a block copolymer which forms a cylindrical morphology andbottlebrush polymer is disposed in a contact hole on a substrate, and islong enough to be vertically placed (i.e. its chain backbone length isgreater than the size of the cylinder phase formed by self-assembly ofthe block copolymer and can thus span across the domains spacing orpitch of the self-assembled block copolymer), it will then scaffold theblock copolymer also within the contact hole to make extended domains ofuninterrupted self-assembled block copolymer, creating a corecylindrical region within the contact hole. The core cylindrical regioncan be etched away later, forming a highly symmetrical and round hole ofa smaller dimension than the original contact hole. The advantages ofthis invention are a much broader process window and a lack of defectscaused by interrupted self-assembled domains within the contact hole.

FIGS. 2(A)-2(F) depicts one of the problems that occurs when disposing ablock copolymer on a substrate. The substrate 100 has disposed thereon aphotoresist 102 with holes 104 of diameter d₁ disposed therein as seenin the FIG. 2(A). The holes are filled with a block copolymer 106 suchas poly(styrene-b-methylmethacrylate) (where “b” stands for block), asseen in the FIG. 2(B). The polymethylmethacrylate forms a cylinder 108(also called a core 108) in the center of the hole, while thepolystyrene 107 surrounds it. The core 108 is then etched away leaving ahole 110 that is then used to facilitate the development of a hole 112in the substrate 100 as seen in the FIG. 2(C). However, in order for thehole 112 to be formed in the substrate, it is desirable to have acontinuous polymethylmethacrylate core that extends from the uppersurface of the block copolymer to the bottom as seen in the FIG. 2(B).This is not always the case depending upon the diameter of the hole inthe photoresist.

As the hole diameter increases from d₁ to d₂ as seen in the FIG. 2(D),the polymethylmethacrylate core 108 does not always form a continuouscylinder 108. In the FIG. 2(E), it can be seen that instead of forming acontinuous cylinder, the polymethylmethacrylate forms a series ofcylindrical discs 114. The formation of these discs is considered adefect in that they prevent the formation of a continuous hole thatextends almost to the substrate as seen in the FIG. 2(F). In summary, ifthe holes in the photoresist are not of the appropriate diameter,defects in the form of missing holes are observed.

It has inadvertently been discovered that by using a composition thatcontains a small amount of a bottlebrush polymer or copolymer inconjunction with a block copolymer, continuous cylindrical domains canbe produced in holes or trenches disposed upon a substrate. Thebottlebrush has an extended backbone (because of the presence of thegrafted polymeric arms that prevent it from behaving like a regularcoiled polymer) that makes it perform like a nano-scale cylinder.Without being limited to theory, it is believed that by designing thebrush polymer to be capable of segregating into the cylinder 108 (seeFIGS. 2(A)-2(F)) and being long enough to extend across the domainsspacing or pitch of the self assembled block copolymer, it can stitchtogether the broken domains. This is demonstrated in the FIGS. 3(A) and3(B), where cylindrical discs 114 are formed when no bottlebrush ispresent (see FIG. 3(A)) and where a continuous cylindrical core 108 isformed when a bottlebrush 116 is embedded within the core of thecylinder phase in a manner where its orientation is perpendicular to thesubstrate (see FIG. 3(B)).

The block copolymer comprises a first polymer and a second polymer,while the additive polymer comprises a bottlebrush copolymer. In oneembodiment, the additive polymer is a bottlebrush polymer that comprisesa single polymer or copolymer that has a free energy (or a surfacetension) that lies between that of the first polymer and the secondpolymer. In another embodiment, the bottlebrush polymer may comprise, asingle polymer that has a surface tension that is equal to the surfacetension of either the first polymer or the second polymer of the blockcopolymer. In this embodiment, the additive polymer may be a polymerthat comprises only a single polymer (where both the chain backbone andthe graft polymers are identical) that is chemically identical with orsubstantially chemically similar to the first polymer of the blockcopolymer or that is chemically identical with or substantiallychemically similar to the second polymer of the block copolymer. Whenthe bottlebrush polymer comprises a single polymer, both the chainbackbone and the graft polymer (the arms) contain the same polymer.

In another embodiment, the additive polymer may be a polymer comprisinga third polymer that is chemically identical with or substantiallychemically similar to the first polymer of the block copolymer and afourth polymer that is chemically identical with or substantiallychemically similar to the second polymer of the block copolymer. Thethird polymer may be the chain backbone while the fourth polymer may bethe graft polymer or alternatively, the third polymer may be the graftpolymer while the fourth polymer may be the chain backbone.

In one embodiment, the additive polymer is a bottlebrush copolymer thatcomprises different polymers where the surface energy (or the surfacetension) of the respective polymers are higher and lower than those ofthe individual polymers of the block copolymer, but where the averagesurface energy of the additive polymer lies between that of the firstpolymer and the second polymer of the block polymer. In one embodiment,the surface energy of the chain backbone (of the bottlebrush polymer)may be higher than that of the first and the second polymer of the blockcopolymer, while the surface energy of the graft polymers (the arms) maybe lower than that of the first and the second polymer of the blockcopolymer. In another embodiment, the surface energy of the graftpolymers (of the bottlebrush polymers) may be higher than that of thefirst and the second polymer of the block copolymer, while the surfaceenergy of the chain backbone may be lower than that of the first and thesecond polymer of the block copolymer.

Prior to being disposed on the substrate, the entire volume of theadditive polymer and the entire volume of the block copolymer areintimately mixed together with a solvent in a vessel and in this blendedstate the domains of the block copolymer are not segregated (i.e., theyare not phase separated and exist in the form of a single homogeneousphase) from each other or from the additive polymer. After beingdisposed on the substrate, the domains of the block copolymer phaseseparate from each other vertically and the additive polymer segregatesinto a domain formed by the block copolymer. In another embodiment,after being disposed on the substrate, the additive polymer segregatesto the free surface of the film (i.e the air-polymer interface) tofacilitate phase separation and vertical alignment of the blockcopolymer.

When the domains of the block copolymer phase separate to formcylinders, the longitudinal axis of the cylinders are perpendicular to asurface of the substrate. In some embodiments, a substrate modificationpolymer is also employed that functions as a substrate modificationlayer of the FIG. 1 and enables the separation of the block copolymerinto vertical cylindrical domains after the composition is disposed on asubstrate. The substrate modification polymer has a reactive groupcapable of bonding with the substrate. By mixing the substratemodification polymer with the block polymer and bottlebrush polymerprior to deposition on a substrate that is to be etched, the substratemodification polymer functions as an embedded substrate modificationlayer—i.e., it separates from the composition after deposition on asubstrate and the reactive group reacts with the substrate. By havingthe substrate modification polymer comprise a polymer that has a surfacetension that lies between the first and the second polymers of the blockcopolymer or by having an substrate modification polymer comprise acopolymer comprising the same or similar polymers as the first andsecond monomers used to form the block copolymer, the composition canfacilitate directed self-assembly of the polymer domains when cast upona substrate. The mixing of the substrate modification polymer with theblock copolymer prior to deposition on a substrate permits the use of aone-step process for manufacturing patterns on substrates.

Disclosed herein too is a method of using the aforementioned compositionto facilitate the directed self-assembly of the polymer domains of thecomposition. The method comprises blending the additive polymer and theblock copolymer together and applying them in a single coating andannealing step or alternatively, in a series of coating and annealingsteps. This method is versatile and robust in that it permits a range ofcompositions (e.g., a range of polymer molecular weights and a range ofweight percents) to be used for the block and additive polymers, whileproviding for better domain alignment than that which can be achieved bythe process depicted in the FIG. 1. Surprisingly, this process not onlysimplifies the process by reducing the number of coat and bake steps,but the process window to achieve good directed self-assembly issignificantly improved over the two-step process that is detailed in theFIG. 1 and that is presently used in industry.

As detailed above, the composition includes a block copolymer and anadditive polymer where the polymers that form the block copolymer areeither similar or substantially similar in chemical character to thepolymers that are used in the additive polymer.

The first polymer and the second polymer are chemically different fromone another and are arranged in blocks in the block copolymer. The blockcopolymer can be a multiblock copolymer. In one embodiment, themultiblocks can include diblocks, triblocks, tetrablocks, and so on. Theblocks can be part of a linear copolymer, a branched copolymer where thebranches are grafted onto a backbone (these copolymers are alsosometimes called “comb copolymers”), a star copolymer, or the like. Theblocks can also be arranged in gradients, where the blocks are arrangedin increasing molecular weight from one end of the polymer chain to theother end. In an exemplary embodiment, the block copolymer is a lineardiblock copolymer. The block copolymer does not have a reactivefunctionality on it when it is contained in the composition.

The first polymer or the second polymer of the block copolymer and ofthe additive polymer are different from one another and may be apolystyrene, a poly(meth)acrylate, a polyacetal, a polyolefin, apolyacrylic, a polycarbonate, a polyester, a polyamide, apolyamideimide, a polyarylate, a polyarylsulfone, a polyethersulfone, apolyphenylene sulfide, a polyvinyl chloride, a polysulfone, a polyimide,a polyetherimide, a polyetherketone, a polyether etherketone, apolyether ketone ketone, a polybenzoxazole, a polyphthalide, apolyanhydride, a polyvinyl ether, a polyvinyl thioether, a polyvinylalcohol, a polyvinyl ketone, a polyvinyl halide, a polyvinyl nitrile, apolyvinyl ester, a polysulfonate, a polysulfide, a polythioester, apolysulfone, a polysulfonamide, a polyurea, a polyphosphazene, apolysilazane, a polybenzothiazole, a polypyrazinoquinoxaline, apolypyromellitimide, a polyquinoxaline, a polybenzimidazole, apolyoxindole, a polyoxoisoindoline, a polydioxoisoindoline, apolytriazine, a polypyridazine, a polypiperazine, a polypyridine, apolypiperidine, a polytriazole, a polypyrazole, a polypyrrolidine, apolycarborane, a polyoxabicyclononane, a polydibenzofuran, apolyphthalide, a polysiloxane, or the like, or a combination comprisingat least one of the foregoing polymers.

Exemplary block copolymers that are contemplated for use include diblockor triblock copolymers such as poly(styrene-b-vinyl pyridine),poly(styrene-b-butadiene), poly(styrene-b-isoprene),poly(styrene-b-methyl methacrylate), poly(styrene-b-alkenyl aromatics),poly(isoprene-b-ethylene oxide), poly(styrene-b-(ethylene-propylene)),poly(ethylene oxide-b-caprolactone), poly(butadiene-b-ethylene oxide),poly(styrene-b-t-butyl (meth)acrylate), poly(methylmethacrylate-b-t-butyl methacrylate), poly(ethylene oxide-b-propyleneoxide), poly(styrene-b-tetrahydrofuran),poly(styrene-b-isoprene-b-ethylene oxide),poly(styrene-b-dimethylsiloxane), poly(styrene-b-trimethylsilylmethylmethacrylate), poly(methyl methacrylate-b-dimethylsiloxane), poly(methylmethacrylate-b-trimethylsilylmethyl methacrylate), or the like, or acombination comprising at least one of the foregoing block copolymers.

In an embodiment, the additive polymer is a bottlebrush polymer orcopolymer where the surface tension of the polymer or copolymer liesbetween the surface tension of the first polymer and that of the secondpolymer. As noted above, the bottlebrush polymer may comprise apolymeric chain backbone and a grafted polymer (that is grafted onto thechain backbone) both of which comprise a single polymer (e.g., a thirdpolymer). In other words, the polymeric chain backbone and the graftpolymer both comprise the third polymer. The third polymer comprisespolymers such as poly(aromatics) and poly(alkenyl aromatics)(polystyrene, poly(t-butylstyrene) poly(2-vinyl pyridine), and thelike), poly(alkyl (meth)acrylates) (poly(methyl methacrylate),poly(ethyl methacrylate), poly(trimethylsilylmethyl methacrylate), andthe like), polybutadiene, polyisoprene, polysiloxanes(polydimethylsiloxane, poly(methylphenylsiloxane); or the like, or acombination thereof. The combination includes the use of two bottlebrushpolymers without them having a bond that links them together. In oneexemplary embodiment, the polymeric chain backbone and the graftedpolymer both comprise either a polystyrene or a polyalkyl(meth)acrylate.

In another embodiment, the bottlebrush polymer can comprise a graftpolymer where the polymeric chain backbone is different from the graftpolymer. The polymeric chain backbone is termed the third polymer whilethe graft polymer is termed the fourth polymer. In one embodiment, apolymer that is used as the polymer chain backbone in one bottlebrushpolymer may be used as the graft polymer in another bottlebrush polymer,while the graft polymer in one bottlebrush polymer may be used as thepolymer chain backbone in another bottlebrush polymer.

In one embodiment, the backbone polymer can be one that comprises astrained ring along the chain backbone. In another embodiment, thebackbone polymer can be a polyacetal, a polyacrylic, a polycarbonate, apolystyrene, a polyester, a polyamide, a polyamideimide, a polyarylate,a polyarylsulfone, a polyethersulfone, a polyphenylene sulfide, apolyvinyl chloride, a polysulfone, a polyimide, a polyetherimide, apolytetrafluoroethylene, a polyetherketone, a polyether etherketone, apolyether ketone ketone, a polybenzoxazole, a polyoxadiazole, apolybenzothiazinophenothiazine, a polybenzothiazole, apolypyrazinoquinoxaline, a polypyromellitimide, a polyquinoxaline, apolybenzimidazole, a polyoxindole, a polyoxoisoindoline, apolydioxoisoindoline, a polytriazine, a polypyridazine, apolypiperazine, a polypyridine, a polypiperidine, a polytriazole, apolypyrazole, a polypyrrolidine, a polycarborane, apolyoxabicyclononane, a polydibenzofuran, a polyphthalide, apolyanhydride, a polyvinyl ether, a polyvinyl thioether, a polyvinylalcohol, a polyvinyl ketone, a polyvinyl halide, a polyvinyl nitrile, apolyvinyl ester, a polysulfonate, a polynorbornene, a polysulfide, apolythioester, a polysulfonamide, a polyurea, a polyphosphazene, apolysilazane, a polyurethane, or the like, or a combination including atleast one of the foregoing polymers. In an exemplary embodiment, thebackbone polymer is polynorbornene. The ring of the polynorbornenerepeat units may, if desired, be substituted with an alkyl group, anaraalkyl group, or an aryl group. In another exemplary embodiment, thebackbone polymer is poly(norbornene-2,3-dicarboximide).

Examples of graft copolymers are poly(styrene-g-vinyl pyridine),poly(vinyl pyridine-g-styrene), poly(styrene-g-butadiene),poly(butadiene-g-styrene), poly(styrene-g-isoprene),poly(isoprene-g-styrene), poly(styrene-g-methyl methacrylate),poly(methyl methacrylate-g-styrene), poly(t-butylstyrene-g-methylmethacrylate), poly(methyl methacrylate-g-t-butylstyrene),poly(styrene-g-alkenyl aromatics), poly(alkenyl aromatics-g-styrene),poly(isoprene-g-ethylene oxide), poly(ethylene oxide-g-isoprene),poly(styrene-g-(ethylene-propylene)),poly(ethylene-propylene)-g-styrene), poly(ethyleneoxide-g-caprolactone), poly(caprolactone-g-ethylene oxide),poly(ethylene oxide-g-caprolactone), poly(butadiene-g-ethylene oxide),poly(ethylene oxide-g-butadiene), poly(styrene-g-t-butyl(meth)acrylate), poly((t-butyl (meth)acrylate)-g-styrene), poly(t-butylmethacrylate-g-methyl methacrylate), poly(ethylene oxide-g-propyleneoxide), poly(propylene oxide-g-ethylene oxide),poly(styrene-g-tetrahydrofuran), poly(tetrahydrofuran-g-styrene),poly(styrene-g-isoprene-g-ethylene oxide),poly(styrene-g-dimethylsiloxane), poly(dimethylsiloxane-g-styrene),poly(t-butylstyrene-g-dimethylsiloxane),poly(dimethylsiloxane-g-t-butylstyrene),poly(styrene-g-trimethylsilylmethyl methacrylate),poly(trimethylsilylmethyl methacrylate-g-styrene), poly(methylmethacrylate-g-dimethylsiloxane), poly(dimethylsiloxane-g-methylmethacrylate), poly(methyl methacrylate-g-trimethylsilylmethylmethacrylate), poly(trimethylsilylmethyl methacrylate-g-methylmethacrylate), poly(norbornene-g-polystyrene),poly(norbornene-g-polymethylmethacrylate),poly(norbornene-g-poly(styrene-r-methylmethacrylate)),poly(norbornene-g-polystyrene-g-polymethylmethacrylate),poly(norbornene-2,3-dicarboximide-g-polymethylmethacrylate),poly(norbornene-2,3-dicarboximide-g-polystyrene),poly(norbornene-g-poly(styrene-r-methylmethacrylate)), or the like, or acombination thereof. The term “combination” includes the use of twobottlebrush copolymers without them having a bond that links themtogether.

In an embodiment, the additive polymer comprises a bottlebrush copolymerthat is chemically identical with the first polymer or the secondpolymer. In other words, the polymer chain backbone (i.e., the thirdpolymer) is chemically similar to the first polymer, while the polymergraft (i.e., the fourth polymer) is chemically similar to the secondpolymer. In this event, the polymers used in the additive polymer may beselected from the list of polymers detailed above. In an embodiment, thepolymer used in the additive polymer is not chemically identical withbut is substantially similar to the first polymer or to the secondpolymer. In other words, the polymer chain backbone (i.e., the thirdpolymer) is not chemically identical with but is substantially similarto the first polymer, while the polymer graft (i.e., the fourth polymer)is not chemically identical with but is substantially similar to thesecond polymer.

The substrate modification polymers are functionalized with a reactivegroup to facilitate bond formation or complexation or coordination withthe substrate that the composition is disposed on. The reactive groupsare detailed below.

In an embodiment, the first polymer of the block copolymer as well asone of the polymer chain backbone or the graft polymer (sometimesreferred to as the third polymer herein) of the additive polymer is avinyl aromatic polymer (e.g., polystyrene or its derivatives), while thesecond polymer as well as the graft polymer of the additive polymer isan ethylenically unsaturated polymer (e.g., an acrylate polymer or itsderivatives). The first polymer and the third polymer is derived from avinyl aromatic monomer having the structure of formula (1):

wherein R⁵ is hydrogen, an alkyl or halogen; Z¹ is hydrogen, halogen, ahydroxyl or an alkyl; and p is from 1 to about 5.

The vinyl aromatic monomers that can be polymerized to produce the firstpolymer of the copolymer of the block copolymer and/or of the additivepolymer are styrenes, alkylstyrenes, hydroxystyrenes or chlorostyrenes.Examples of suitable alkylstyrenes are o-methylstyrene, p-methylstyrene,m-methylstyrene, α-methylstyrene, o-ethylstyrene, m-ethylstyrene,p-ethylstyrene, α-methyl-p-methylstyrene, 2,4-dimethylstyrene,p-tert-butylstyrene, 4-tert-butylstyrene, or the like, or a combinationcomprising at least one of the foregoing alkylstyrene monomers. Anexemplary first polymer (for the block copolymer) and for the polymericchain backbone of the additive polymer is polystyrene orpoly(4-tert-butylstyrene).

As noted above, the first polymer of the block copolymer can be eithersimilar or substantially similar in chemical character to a thirdpolymer that is used in the additive polymer. When the first polymer ofthe block copolymer is substantially similar in chemical character to athird polymer that is used in the additive polymer, the first polymer ofthe block copolymer can be one of a styrene, an alkylstyrene, ahydroxystyrene or a chlorostyrene, while the third polymer of theadditive polymer can be one of a styrene, an alkylstyrene, ahydroxystyrene or a chlorostyrene so long as the first polymer of theblock copolymer is not chemically identical with the third polymer ofthe additive polymer. In other words, while the first polymer of theblock copolymer is not chemically identical with the third polymer ofthe additive polymer, the two form polymers that are chemicallycompatible with one another (i.e., they are miscible with one another inall proportions).

The molecular weight of the first polymer of the block copolymer isselected based upon the target pitch of the copolymer when it isdisposed upon a substrate. The pitch is the average center to centerdistance between successive domains of a particular block when thecomposition is disposed upon a substrate. The pitch generally increaseswith increasing molecular weight and so controlling the molecular weightof the first polymer can be used to control the pitch. In a preferredembodiment, the weight average molecular weight (M_(w)) of the firstpolymer is about 2 kg/mol to about 200 kg/mol, specifically about 5kg/mol to about 100 kg/mol and more specifically about 7 kg/mol to about50 kg/mol grams per mole as measured by multi-angle laser lightscattering (MALLS) gel permeation chromatography (GPC) instrument usingTHF as the mobile phase at a flow of 1 milliliter per minute (mL/min).

The polydispersity index of the first polymer is less than or equal toabout 1.20, specifically less than or equal to about 1.10 andspecifically less than or equal to about 1.08 when determined by sizeexclusion chromatography (SEC) with chloroform as the mobile phase (at35° C. and a flow rate of 1 mL/min).

The second polymer of the block copolymer as well as one of the polymerchain backbone or the graft polymer (also known as the fourth polymerherein) of the additive polymer is derived from the polymerization of anacrylate monomer. In one embodiment, the second polymer and the fourthpolymer is obtained from the polymerization of units having a structurerepresented by formula (2):

where R₁ is a hydrogen or an alkyl group having 1 to 10 carbon atoms.Examples of the first repeat monomer are acrylates and alkyl acrylatessuch as α-alkyl acrylates, methacrylates, ethacrylates, propylacrylates, butyl acrylate, or the like, or a combination comprising atleast one of the foregoing acrylates.

In one embodiment, the second polymer or the fourth polymer has astructure derived from a monomer having a structure represented by theformula (3):

where R₁ is a hydrogen or an alkyl group having 1 to 10 carbon atoms andR₂ is a C₁₋₁₀ alkyl, a C₃₋₁₀ cycloalkyl, or a C₇₋₁₀ aralkyl group.Examples of the (α-alkyl)acrylates are methacrylate, ethacrylate, propylacrylate, methyl methacrylate, ethyl methacrylate, propyl methacrylate,or the like, or a combination comprising at least one of the foregoingacrylates. The term “(α-alkyl)acrylate” implies that either an acrylateor (α-alkyl)acrylate is contemplated unless otherwise specified.

As noted above, the second polymer of the block copolymer can be eithersimilar or substantially similar in chemical character to one of thethird or the fourth polymer that is used in the additive polymer or tothe single polymer that is used in the additive polymer (when thepolymer chain backbone and the graft polymer are identical incomposition). In an embodiment, the second polymer of the blockcopolymer can be one of an acrylate or an alkyl acrylate, while one ofthe third or the fourth polymer of the additive polymer can be one of anacrylate or an alkyl acrylate so long as the second polymer of the blockcopolymer is not chemically identical with the third or the fourthpolymer of the additive polymer. In other words, while the secondpolymer of the block copolymer is not chemically identical with thethird and the fourth polymer of the additive polymer, the two arechemically compatible with one another (i.e., they are miscible with oneanother in all proportions).

The weight average molecular weight (M_(w)) of the second polymer isabout 2 kg/mol to about 200 kg/mol, specifically about 5 kg/mol to about100 kg/mol and more specifically about 7 kg/mol to about 50 kg/mol gramsper mole as measured by multi-angle laser light scattering (MALLS) gelpermeation chromatography (GPC) instrument using THF as the mobile phaseat a flow of 1 milliliter per minute (mL/min). The polydispersity indexof the second polymer is less than or equal to about 1.20, specificallyless than or equal to about 1.10 and specifically less than or equal toabout 1.08 when determined by size exclusion chromatography (SEC) withchloroform as the mobile phase (at 35° C. and a flow rate of 1 mL/min).In order to convert a weight average molecular weight to a numberaverage molecular weight, the weight average molecular weight asmeasured by gel permeation chromatography (GPC) instrument using THF asthe mobile phase at a flow of 1 milliliter per minute (mL/min) isdivided by the polydispersity index as determined by size exclusionchromatography (SEC) with chloroform as the mobile phase (at 35° C. anda flow rate of 1 mL/min).

When hole or post patterns (when the block copolymer phase segregates toform cylinders) are desired, the block copolymer is selected from acomposition and molecular weight that result in formation of acylindrical morphology when disposed singularly on a substrate andannealed to form domains. The first polymer is present in the firstblock copolymer in an amount sufficient to form a cylindricalmorphology, in an amount of 15 to 35 wt %, specifically 20 to 30 wt %,based on the total weight of the block copolymer. Accordingly, thesecond polymer is present in the first block copolymer in an amount of85 to 65 wt %, specifically 80 to 70 wt %, based on the total weight ofthe block copolymer.

The polydispersity index of the block copolymer is less than or equal toabout 1.20, specifically less than or equal to about 1.15 andspecifically less than or equal to about 1.10 when determined by sizeexclusion chromatography (SEC) with chloroform as the mobile phase (at35° C. and a flow rate of 1 mL/min).

The weight average molecular weight of the block copolymer is about 2 toabout 200, more specifically about 3 to about 150 kilograms per mole asdetermined using multi-angle laser light scattering gel permeationchromatography and the polydispersity index. In an exemplary embodiment,it is desirable for the block copolymer to have a weight averagemolecular weight of about 5 to about 120 kilograms per mole.

The block copolymer has an interdomain spacing as measured by smallangle xray scattering of less than or equal to about 60 nanometers,specifically less than or equal to about 50 nanometers, morespecifically less than or equal to about 40 nanometers.

In an embodiment, the composition may comprise two or more blockcopolymers—a first block copolymer, a second block copolymer, a thirdblock copolymer, and so on, where each block copolymer has a differentmolecular weight or volume percent. In an exemplary embodiment, thecomposition may comprise two block copolymers—a first block copolymerand a second block copolymer, each of which comprise the same firstpolymer and the same second polymer, but where the first block copolymerhas a different molecular weight or volume percent from the second blockcopolymer. In an embodiment, the first block copolymer has a lowermolecular weight than the second block copolymer.

In another embodiment, the composition may comprise two or more blockcopolymers—a first block copolymer and a second block copolymer, whereat least one of the polymers—either the first polymer and/or the secondpolymer of the first block copolymer are not chemically identical withthe first polymer and/or second polymer of the second block copolymerbut are chemically compatible with one another (i.e., they are misciblewith one another in all proportions). For example, the composition maycomprise two block copolymers and the additive polymer. The first blockcopolymer comprises polystyrene and polymethylmethacrylate blocks, whilethe second block copolymer comprises polyhydroxystyrene andpolymethylmethacrylate and has a different molecular weight from thefirst block copolymer. The additive polymer can comprise, for example, apolystyrene chain backbone and a polymethylmethacrylate orpolyethylmethacrylate graft polymer. In an exemplary embodiment, thecomposition comprises two block copolymers having identical firstpolymers and identical second polymers but having different molecularweights.

The block copolymer is present in the composition in an amount of 80 to99 wt %, preferably 85 to 98 wt %, based on the total weight of theblock copolymer and the additive polymer in the composition. In anexemplary embodiment, the block copolymer is present in an amount of 90to 97 wt %, based on the total weight of the block copolymer and theadditive polymer in the composition.

As detailed above, in one embodiment, the substrate modification polymercomprises at least two polymers (one being the polymeric chain backboneand the other being the polymer graft that is grafted onto the chainbackbone) that are chemically identical to the two polymers of the blockcopolymer, but that are arranged in the form of a bottlebrush polymer.In another embodiment, one or both polymers of the substratemodification polymer can be chemically different from one or bothmonomers used to make the block copolymer but their respective polymershave a chemical affinity (i.e., they are miscible with one another inall proportions) for the one or both polymers of the block copolymer.The substrate modification polymer generally has one or more reactivegroups that can facilitate a reaction with the substrate (i.e., betweenthe additive polymer and the substrate) but does not undergo reactionwith itself or other components of the additive polymer (in other words,it does not become crosslinked after processing on the substrate). Inthis fashion, the substrate modification polymer forms a brush layerwith self-limiting thickness. The substrate modification polymer alsodoes not undergo any reaction with the block copolymer. In an exemplaryembodiment, the reactive end group can be a hydroxyl moiety, an estermoiety, a carboxylic acid moiety, an amine moiety, a thiol moiety, orthe like.

When the additive polymer is a bottlebrush polymer, the polymeric chainbackbone has a weight average molecular weight of 1000 to 100000 gramsper mole, preferably 5000 to 50000 grams per mole. The graft polymer hasa weight average molecular weight of 500 to 100000 grams per mole,preferably 1000 to 20000 grams per mole. The graft polymer may bedisposed along the entire length of the polymeric chain backbone oralong only a portion of the polymeric chain backbone. The averagemolecular weight between successive grafts disposed on the polymericchain backbone is 100 to 500 grams per mole. In an exemplary embodiment,the graft polymer may be disposed along the entire length of thepolymeric chain backbone.

When the additive polymer is a bottlebrush copolymer, the polymericchain backbone is present in an amount of 90 to 50 mol %, specifically75 to 50 mol %, based on the total moles of backbone and graft polymer.Accordingly, the graft polymer is present in the copolymer in an amountof 10 to 50 mol %, specifically 25 to 50 mol %, based on the total molesof backbone and graft polymer. In an exemplary embodiment, if thebottlebrush is a homopolymer of the macromonomer, then the molar ratioof backbone to graft is 1:1.

The polydispersity index of the polymer chain backbone is less than orequal to about 3, specifically less than or equal to about 2 andspecifically less than or equal to about 1.50 when determined by sizeexclusion chromatography (SEC) with tetrahydrofuran or chloroform as themobile phase (at 35° C. and a flow rate of 1 mL/min). The polydispersityindex of the graft polymer is less than or equal to about 3,specifically less than or equal to about 2 and specifically less than orequal to about 1.50 when determined by size exclusion chromatography(SEC) with tetrahydrofuran or chloroform as the mobile phase (at 35° C.and a flow rate of 1 mL/min).

The weight average molecular weight of the bottlebrush polymer is about10 to about 1000 kilograms per mole, more specifically about 50 to about500 kilograms per mole as determined using multi-angle laser lightscattering gel permeation chromatography and the polydispersity index.In an exemplary embodiment, it is desirable for the bottlebrush polymerto have a weight average molecular weight of about 80 to about 300kilograms per mole.

The additive polymer is present in the composition in an amount of 1 to20 wt %, specifically 2 to 15 wt % and 3 to 10 wt %, based on the totalweight of the block copolymer and the additive polymer in thecomposition.

In an embodiment, the substrate modification polymer functions as anembedded substrate modification layer (when disposed on a substrate) andcan be characterized as having a surface tension that lies between theindividual surface tension of the respective polymers that comprise theblocks of the block copolymer. In other words, the surface free energyof the additive polymer lies between the surface free energy of thefirst polymer and the second polymer of the block copolymer.

In one embodiment, the surface modification layer comprises a substratemodification polymer comprising two or more monomeric or polymericrepeat units that have difference in surface energy of 0.01 to 10milli-Newton per meter (mN/m), specifically 0.03 to 3 mN/m, and morespecifically 0.04 to 1.5 mN/m. For example, neutral layers forpolystyrene and polymethylmethacrylate usually comprise styrene andmethylmethacrylate, which only have a difference in surface energy of0.04 mN/m from the respective blocks.

In an embodiment, it is desirable for the substrate modification polymerto form a film with balanced surface tension between the blocks of theblock copolymer. Good results are achieved when the surface tensions areequal. This is the only desired feature and a number of materials canachieve this end result.

In an embodiment, the substrate modification polymer comprises a polymerthat comprises a reactive functional group that can react with afunctional group upon the surface of the substrate to form a brush onthe substrate. The substrate modification polymer is then described asbeing in the form of a brush on the surface of the substrate.

The substrate modification polymer has a lower number average molecularweight than that of the block copolymer and can comprise a differentnumber of moles of the first monomer or polymer (also called the thirdpolymer) and the second monomer or polymer (also called the fourthpolymer) when compared with the block copolymer.

In an exemplary embodiment, the substrate modification polymer has anumber average molecular weight of 5 to 100 kilograms per mole,preferably 7 to 50 kilograms per mole. The polydispersity index for thesubstrate modification polymer is 1.05 to 2.5, preferably 1.10 to 1.60.When the block copolymer is PS-block-PMMA, the substrate modificationpolymer can be a copolymer of styrene and methylmethacrylate (i.e., apoly(styrene-r-methylmethacrylate)) and comprise 28 to 70 mole percent,preferably 32 to 65 mole percent of polystyrene based on the totalnumber of moles of the substrate modification polymer present in thecomposition.

Exemplary substrate modification polymers are hydroxyl end-functionalpoly(styrene-r-methylmethacrylate) (where the “r” between the styreneand the methacrylate stands for “random”) or poly(styrener-methylmethacrylate-r-hydoxyethyl methacrylate).

The block copolymer, the additive polymer, and the substratemodification polymer can be manufactured in a batch process or in acontinuous process. The batch process or the continuous process caninvolve a single or multiple reactors, single or multiple solvent andsingle or multiple catalysts (also termed initiators).

In one embodiment, the block copolymer can contain anti-oxidants,anti-ozonants, mold release agents, thermal stabilizers, levelers,viscosity modifying agents, free-radical quenching agents, otherpolymers or copolymers such as impact modifiers, or the like. Thecomposition can also include an embedded neutral layer to facilitateperpendicular domain orientation in block copolymers having a largemismatch in surface tension of the first and second blocks. In someembodiments, the bottlebrush polymer can also function as an embeddedneutral layer.

In the preparation of the additive polymer, the third monomer (fromwhich the third polymer is obtained) and/or the fourth monomer (fromwhich the fourth polymer is obtained), the solvent(s) and initiators areadded to the reaction vessel in the desired ratios. The contents of thevessel are subjected to heat and agitation to produce the additivepolymer. The additive polymer is then precipitated from solution andsubjected to further processing as is detailed below.

The block copolymer and the additive polymer after purification may bedissolved in a solvent and then disposed upon the surface of a substrateto form a block copolymer film whose blocks are perpendicular inorientation to the surface of the substrate. In one embodiment, thesurface of the substrate may contain a brush or crosslinked mat as anoptional surface modification layer disposed thereon prior to thedisposing of the block copolymer onto the surface of the substrate.

In one embodiment, the substrate may contain a layer of a polymer thatis crosslinked after being disposed upon the substrate. The layer isformed by disposing a polymer having reactive substituents along thechain backbone capable of reacting either with itself or acrosslink-inducing additive to form bonds or crosslinks betweenindividual chains of the polymer after it is disposed upon thesubstrate. A layer crosslinked in this manner is then described as beingin the form of a mat or mat-like film on the surface of the substrate.This is distinguished from the bottlebrush polymer, which is notcrosslinked on or reacted with the substrate.

The substrate can also be patterned such that some areas result inperpendicular orientation while others induce a parallel orientation ofthe domains of the composition. The substrate can also be patterned suchthat some regions selectively interact, or pin, a domain of the blockcopolymer to induce order and registration of the block copolymermorphology. The substrate can also have topography that induces thealignment and registration of one or more of the domains of thecomposition. The composition after being disposed upon the substrate isoptionally heated to a temperature of up to 350° C. for up to 4 hours toboth remove solvent and to form the domains in an annealing process.Preferred annealing temperatures are dependent on the specificcomposition of the polymers employed. Generally, annealing is conductedat a temperature above the highest glass transition temperature of theblock copolymer but below the order-disorder transition temperature(i.e. the temperature at which the block copolymer undergoes atransition from an ordered, phase separated state to a homogeneous melt)and the decomposition temperature of the polymers. When PS-b-PMMA isemployed as the block copolymer, annealing is generally conductedbetween 180 to 300° C. The annealing of the composition can be used tovary the interdomain spacing (i.e., the periodicity) of the cylindricaland/or lamellar domains. The size of the domains can also be varied byannealing.

The solvent that the composition is dissolved in prior to being disposedupon the substrate may be one of those listed above. Examples of usefulsolvents for compatibilizing the composition are propylene glycolmonomethyl ether acetate, propylene glycol monomethyl ether, toluene,anisole, n-butylacetate, isobutylisobutyrate, benzyl benzoate,cyclohexanone, methyl-2-hydroxyisobutryate, gamma-butyrolactone,propylene glycol ethyl ether, ethyl lactate, and the like. A preferredsolvent is propylene glycol monomethyl ether acetate.

The domains of the block copolymer upon annealing form perpendicular tothe substrate and the first polymer aligns to the pattern created on thefirst domain to the “pinning” feature on the substrate, and the secondpolymer forms a second domain on the substrate aligned adjacent to thefirst domain. One of the domains of the block copolymer (formed fromeither the first polymer of the copolymer or the second polymer of thecopolymer) may then be preferentially etched away. A relief pattern isthen formed by removing either the first or second domain to expose anunderlying portion of the surface modification layer. In an embodiment,removing is accomplished by a wet etch method, developing, or a dry etchmethod using a plasma such as an oxygen plasma. The block copolymer withat least one domain removed is then used as a template to decorate ormanufacture other surfaces that may be used in fields such aselectronics, semiconductors, and the like.

The invention is further illustrated by the following non-limitingexamples.

EXAMPLES

The following examples are paper examples that demonstrate than when thecomposition contains a block copolymer and a bottlebrush polymer orcopolymer, defects are minimized and cylindrical domains that extendthrough most of the length of the hole (in the photoresist) areproduced. We performed self-consistent field theory (SCFT) simulationson various DSA scenarios for linear diblock copolymers and blends oflinear diblocks with bottlebrush polymers. We explored the defectformation energy of a common defect mode as a function of hole size todetermine the hole size process window over which low defectivity couldbe expected. In these simulations, we seed in a defect structure andcalculate its free energy, F_(defect), and compare that to the freeenergy of the defect-free state, F_(ideal). The difference in energy ofthese two states is defined as the defect formation free energy,ΔF_(defect):ΔF _(defect) =F _(defect) −F _(ideal)  (1)

Both the linear AB diblock copolymers and the bottle brush copolymersand homopolymers are modeled with the continuous Gaussian chain model(see: Fredrickson, G. H.; “The Equilibrium Theory of InhomogeneousPolymers.” Clarendon Press, Oxford, 2006). The linear AB diblockcopolymer is assumed to contain a total of N statistical segments, afraction f of which are species A. The backbone of the bottle brushpolymer is comprised of species C and has N_(C) statistical segments,while grafted arms of species A and B have, respectively, N_(A) andN_(B) statistical segments. The diblock chain length N is used as areference chain length; the symbol α is used to denote relative chainlengths of the backbone and grafted arms of the bottle brush relative tothe diblock length. The grafts (side arms) along the backbone areassumed to be uniformly spaced, with the number of grafts per scaledlength of the backbone denoted by σ and fixed at a value of 50, which isrepresentative of the experimental examples. Through-space distances aremeasured in units of the unperturbed radius of gyration, R_(g), of thediblock copolymer.

The binary contact interactions between polymer statistical segments aredescribed using Flory-Huggins parameters. The A-B segmental interactionis denoted by χ, the interactions between A or B segments and theconfinement boundaries or “walls” in the simulation are denoted byχ_(wA) or χ_(wB), respectively, and the interactions between thebackbone C of the bottle brush and the other segment types and walls isdenoted χ_(C-other). Since the C backbone is largely shielded by itssurrounding grafts at the high grafting densities considered here, thesimulations prove insensitive to χ_(C-other), so we set all suchinteraction strengths to zero for convenience. Finally, the polymer meltis assumed to be nearly incompressible, so that the sum of A, B, C, andwall densities is uniform in the system.

In summary, the SCFT model and simulation results are described by thefollowing parameters:

χN Segregation strength of the AB diblock copolymer R_(g) Radius ofgyration of the AB diblock copolymer—the reference lengthscale fordomain sizes and periods and confinement dimensions. χ_(w)N = (χ_(wA)N −Segregation strength that controls the relative attraction of χ_(wB)N)/2A or B polymer segments (of either diblock or bottle brush) to the wallf Volume fraction of the minority A block of the linear AB diblockcopolymer χ_(Backbone-other)N Segregation strength of the backbone ofthe bottlebrush from the other polymer components in the system. Chosenhere to be zero. α_(backbone) Bottlebrush backbone length scaledrelative to the linear AB diblock copolymer length, N_(C)/N α_(sidearm)A or B graft length of the bottlebrush polymer scaled relative to thelinear AB diblock copolymer length, N_(A)/N or N_(B)/N σ Graftingdensity: the number of grafted arms per scaled length of the bottlebrushbackbone, α_(backbone). Chosen here to be 50. CD_(guide) Criticaldimension of the guide hole

Algorithms for conducting SCFT simulations of such polymer blend modelsare described in the monograph, Fredrickson, G. H.; “The EquilibriumTheory of Inhomogeneous Polymers.” Clarendon Press, Oxford, 2006. Amodel and algorithm specific to the confined DSA simulations reportedhere are described in the publication “Microdomain Ordering in LaterallyConfined Block Copolymer Thin Films”, A. W. Bosse, C. J. Garcia-Cervera,and G. H. Fredrickson, Macromolecules 40, 9570 (2007). A computer codefor conducting SCFT simulations of both bulk and confined polymersystems, PolyFTS, is available for license from the University ofCalifornia, Santa Barbara.

Comparative Example A

This is a comparative example that demonstrates behavior of a A-B linearblock copolymer disposed and annealed in a contact hole (i.e. contacthole shrink). This example does not contain a bottlebrush polymer. It isa paper example that is based off of calculations using self-consistentfield theoretical simulations. The structures and defect formationenergies for a hole shrink with a linear PS-b-PMMA diblock copolymerwere calculated. For the simulation, the following parameters werechosen: PS-b-PMMA was the block copolymer, f_(PMMA)=0.3, χN=25,χ_(w)N=−32 (minor block A attractive, e.g., PMMA in PS-b-PMMA), and theradius of gyration Rg=7.2 nm. CD_(guide) was varied from 8 to 10 Rg andthe hole depth=15 Rg. The calculated structures of the ideal morphologyand the “four bead defect” commonly observed for this type of DSA whenCD_(guide) deviates from the ideal size are respectively shown in FIGS.5(A) and 5(B). These structures were calculated for a range of hole CD,and the defect formation energy was then calculated. FIG. 6 shows thedefect formation energy (of the four bead defect) as a function of holeCD. When CD_(guide)=10 Rg, the defect formation energy reaches a maximumvalue of ˜50 kT. However, the defect formation energy rapidly declinesas CD_(guide) moves away from this optimal value, indicating that lowdefectivity would only occur across a narrow range of CD_(guide) valuescentered around 10 Rg.

Example 1

This is a paper example that demonstrates hole shrink with linearPS-b-PMMA diblock copolymer/bottlebrush polymer blends. Structures anddefect formation energies for hole shrink with a blend of a linearPS-b-PMMA diblock copolymer and a polymethylmethacrylate (PMMA)bottlebrush polymer were calculated. The PMMA bottlebrush polymer has apolymeric chain backbone and graft polymers both of which comprise PMMA.For the simulation, the following parameters were chosen: PS-b-PMMA wasthe block copolymer, 10 volume percent (%) PMMA bottlebrush was added tothe diblock copolymer, χN=25, χ_(Backbone-other)N=0, χ_(w)N=−32 (PMMAattractive), α_(Sidearm)=0.1, α_(Backbone)=0.6, 1.2, 1.8 and 2.4, andthe grafting density was chosen to be 50. CD_(guide) was varied from 8to 10 Rg, and hole depth=15 Rg. Whereas the linear diblock had a defectformation energy of 50 kT at CD=10 Rg and a steep decline away from thisoptimal CD_(guide) value (FIG. 6), the blends of linear diblock andbottlebrush resulted in an unstable defect that immediately healed tothe ideal state across a wide range of CD_(guide). This effect wasobserved for bottlebrushes at all studied backbone lengths(α_(Backbone)=0.6, 1.2, 1.8 and 2.4). Since the defect was immediatelyhealed, the defect state is inherently unstable, so no defect formationenergy can be calculated. From these simulation results, addition of thebottlebrush gave a much wider process window for DSA relative to thelinear diblock of Comparative Example A alone.

Example 2

This is another paper example that demonstrates the effect ofbottlebrush loading, i.e. volume fraction in the blend, on hole shrinkwith linear PS-b-PMMA diblock copolymer/bottlebrush polymer blends.

Structures and defect formation energies for hole shrink with a blend ofa linear PS-b-PMMA diblock copolymer and a PMMA bottlebrush werecalculated, this time with varying loading of the bottlebrush. For thesimulation, the following parameters were chosen: PS-b-PMMA was theblock copolymer, χN=25, χ_(Backbone-other)N=0, χ_(w)N=−32 (PMMAattractive), α_(Backbone)=2.4, grafting density of 50, CD_(guide)=10 Rg,and hole depth=15 Rg. Three values of bottlebrush arm length wereexamined, α_(Sidearm)=0.05, 0.1, and 0.2, and bottlebrush loading wasvaried from 0 to 10 volume %. Defect formation energy as a function ofbottlebrush loading is shown in FIG. 7. For all studied bottlebrushlengths, defect formation energy increased immediately with only 1 vol %bottlebrush and increased further with continuing addition ofbottlebrush until the defects became unstable and melted to the perfectstate, at which point the defect formation energies were incalculable.The bottlebrush with shortest arms, α_(sidearm)=0.05, showed the highestdefect formation energies and resulted in totally unstable defects atthe lowest volume percentage.

Example 3

This is another paper example that demonstrates the effect ofbottlebrush grafting density on hole shrink with linear PS-b-PMMAdiblock copolymer/bottlebrush polymer blends. Structures and defectformation energies for hole shrink with a blend of a linear PS-b-PMMAdiblock copolymer and a PMMA bottlebrush were calculated, this time withvarying the grafting density of the bottlebrush. For the simulation, thefollowing parameters were chosen: PS-b-PMMA was the block copolymer,χN=25, χ_(Backbone-other)N=0, χ_(w)N=−32 (PMMA attractive),α_(Sidearm)=0.1, α_(Backbone)=2.4, 4 vol % bottlebrush, CD_(guide)=10Rg, and hole depth=15 Rg. Four values of bottlebrush grafting densitywere examined, 25, 33, 50, 66 and 75. Defect formation energy as afunction of grafting density is shown in FIG. 7. At a grafting densityof 25, the defect was unstable and immediately healed to the perfectstate. As grafting density increased to 33 and above, the defectformation energies were calculable and decreased slightly from 145 to116 kT. However, all cases were much higher than the case withoutbottlebrush in Comparative Example A, which showed a defect formationenergy of 52.5 kT.

Example 4

This is another paper example that details hole shrink with compositionsthat comprise linear PS-b-PMMA diblock copolymer/bottlebrush polymerblends. Structures and defect formation energies for hole shrink with ablend of a linear PS-b-PMMA diblock copolymer and both polystyrene (PS)and polymethylmethacrylate (PMMA) polymeric bottlebrushes. For thesimulation, the following parameters were chosen: PS-b-PMMA was theblock copolymer, χN=25, χ_(Backbone-other)N=0, χ_(w)N=−32 (PMMAattractive), α_(Sidearm)=0.1, α_(Backbone)=2.4, grafting density=50,CD_(guide)=10 Rg, and hole depth=15 Rg. Various vol % of both PS andPMMA bottlebrushes were added, and the (“four bead”) defect formationenergies of the corresponding ternary blends are summarized in Table 1below. Results for binary blends with PMMA-bottlebrushes (BB) andPS-bottlebrushes are shown in the FIG. 8; PMMA-BB was more effectivethan the PS-BB at increasing the defect formation energy, although bothadditives did increase the energy over the baseline with no added BB. Ata constant loading of PMMA-BB, increasing the volume of PS-BB caused thedefects to become slightly less costly until the point that they loststability. This data shows that blends of linear PS-b-PMMA diblock andboth PS-BB and PMMA-BB have better defectivity properties than purelinear diblock copolymers.

Table 1 shows defect formation energy for a linear AB diblock copolymerblended with various amounts of PS-BB and PMMA-BB in a cylindricalprepattern with PMMA-block-attractive walls and substrate. Cells withoutnumbers indicate the defects were unstable and thus their formationenergy was incalculable.

TABLE 1 PS-BB (vol %) Vol % 0 1 2 3 4 5 6 7 8 9 10 PMMA- 0  52  80  82 84 85 86 86 85 84 83 82 BB 1  95  95  96  93 91 88 86 — — — — (vol %) 2111 113 112 100 96 — — — — — — 3 123 115 111 107 — — — — — — — 4 139 — —— — — — — — — — 5 140 — — — — — — — — — — 6 — — — — — — — — — — — 7 — —— — — — — — — — — 8 — — — — — — — — — — — 9 — — — — — — — — — — — 10 — —— — — — — — — — —

Comparative Example B

This is a paper example that demonstrates the effect of bottlebrushgrafting density on line/space graphoepitaxy with linear diblockcopolymer/bottlebrush polymer blends. In this comparative example,structures and defect formation energies for line/space graphoepitaxywith a linear PS-b-PDMS diblock copolymer were calculated. For thesimulation, the following parameters were chosen: PS-b-PDMS was theblock copolymer, χN=33 (corresponding to PS-b-PDMS with M_(n)(PS)=44kg/mol and M_(n)(PDMS)=14 kg/mol), χ_(w)N=32 (minor block PDMSattractive walls), and trench depth=3 Rg (where Rg=6.6 nm). Structuresand defect formation energies for the block copolymer in trenchesdesigned to hold four cylinders were calculated. PDMS density maps ofthe ideal state and a representative “disclination type” defect areshown in FIG. 9. Trench width was varied to study the impact of trenchwidth on defect formation energy, and the results are plotted in FIG.10. A defect formation energy of >30 kT is required to achieve thedesired defect density of <0.01 defects per cm². For the linear diblock,the defect formation energy reached a maximum of 48 kT at a trench widthof 17.4 Rg, and the defect formation energy declined as the trenchvaried away from this optimal value. The process window, defined as therange of trench width for which the defect formation energy was abovethe 30 kT threshold, was approximately 5 Rg.

Example 5

This is a paper example that demonstrates the effect of bottlebrushgrafting density on line/space graphoepitaxy with linear diblockcopolymer/bottlebrush polymer blends. Structures and defect formationenergies for line/space graphoepitaxy with a blend of a linear PS-b-PDMSdiblock copolymer and a bottlebrush polymer with PS arms werecalculated. For the simulation, the following parameters were chosen:PS-b-PDMS was the block copolymer, χN=33 (corresponding to PS-b-PDMSwith M_(n)(PS)=44 kg/mol and M_(n)(PDMS)=14 kg/mol),χ_(Backbone-other)N=0, χ_(n)N=−32 (minor block PDMS attractive),α_(Sidearm)=0.1, α_(Backbone)=0.6, grafting density=50, 10 vol % BB,trench depth=3 Rg (where Rg=6.6 nm). The structures and defect formationenergies for the block copolymer in trenches designed to hold fourcylinders were calculated. Trench width was again varied to study theimpact of trench width on defect formation energy, and the results areplotted in FIG. 11. A defect formation energy of >30 kT is required toachieve the desired defect density of <0.01 defects per cm².

For the case of the bottlebrush with PS arms, the maximum defectformation energy was lower (35 kT) than for the linear diblock inComparative Example B (48 kT), and the optimal trench width increased to19.2 Rg. The defect formation energy again decreased as the trenchvaried away from this optimal value. The process window, defined as therange of trench width for which the defect formation energy was abovethe 30 kT threshold, was approximately 3 Rg. This shows that adding abottlebrush polymer comprising arms that are similar in chemistry tothose of the majority block, i.e., PS-BB into a PS-b-PDMS diblock withmajority PS, gives worse DSA results in a line/space configuration thanthe neat linear diblock alone.

Example 6

This is another paper example that details the effect of bottlebrushgrafting density on line/space graphoepitaxy with linear diblockcopolymer/bottlebrush polymer blends. Structures and defect formationenergies for line/space graphoepitaxy with a blend of a linear PS-b-PDMSdiblock copolymer and a bottlebrush polymer with PDMS arms werecalculated. For the simulation, the following parameters were chosen:PS-b-PDMS was the block copolymer, χN=33 (corresponding to PS-b-PDMSwith M_(n)(PS)=44 kg/mol and M_(n)(PDMS)=14 kg/mol),χ_(Backbone-other)N=0, χ_(w)N=−32 (minor block A attractive),α_(Sidearm)=0.1, α_(Backbone)=0.6, grafting density=0.5, and trenchdepth=3 Rg (where Rg=6.6 nm). Structures and defect formation energiesfor the block copolymer in trenches designed to hold four cylinders werecalculated. Two different loadings of the PDMS bottlebrush, 4 vol % and10 vol %, were examined. Trench width was again varied to study theimpact of trench width on defect formation energy, and the results areplotted in FIG. 10.

When 10 vol % of the PDMS bottlebrush was added to the composition, thedefects became unstable and were immediately healed to a perfect state.In other words, the cast composition was defect free. Accordingly, thedefect formation energy could not be calculated. At only 4 vol % PDMSbottlebrush content in the composition, the maximum defect formationenergy was higher (52 kT) than for only the linear diblock inComparative Example B (48 kT), and the optimal trench width increased to20 Rg. The defect formation energy again declined as the trench variedaway from this optimal value, but the process window where the energywas above 30 kT was approximately 7 Rg, larger than for the lineardiblock alone in Comparative Example B (5 Rg).

This data shows adding bottlebrush with minority block preferentialarms, i.e., PDMS-BB into a PS-b-PDMS diblock with majority PS, improvesboth the defect density and process window for line/space graphoepitaxyDSA when compared to the neat linear diblock alone.

Example 7

This is another paper example that details the effect of addingbottlebrush grafting density on line/space graphoepitaxy with lineardiblock copolymer/bottlebrush polymer blends. Structures and defectformation energies for line/space graphoepitaxy with blend of a linearPS-b-PDMS diblock copolymer and various loadings of bottlebrush polymerswith both PDMS arms (PDMS-BB) and PS arms (PS-BB). For the simulations,the following parameters were chosen: PS-b-PDMS was the block copolymer,χN=33 (χN was scaled by ⅓ for stable SCFT simulations from 100, whichcorresponds to PS-b-PDMS with M_(n)(PS)=44 kg/mol and M_(n)(PDMS)=14kg/mol), χ_(n)N=−32 (minor block PDMS attractive walls), Lx(longitudinal length along the cylinders)=24 Rg, Lz (total depth,polymer filling level)=8 Rg and trench depth=3 Rg (where Rg=6.6 nm). TheRg and energy units are converted from the original χN=100. Wecalculated structures and defect formation energies for the blockcopolymer in trenches designed to hold four cylinders. The trench widthwas fixed to 20 Rg at which the blend with 4 vol % of PDMS-BB maximizesthe defect formation energy. Various vol % of both PS and PDMSbottlebrushes were added, and the defect formation energies aresummarized in Table 2. PDMS-BB was more effective than the PS-BB atincreasing the defect formation energy, although both additives didincrease the energy over the baseline with no added BB until 6 vol % ofPS-BB was added. Blends of linear diblock and only PDMS-BB gave thelargest increases in defect formation energy but adding PS-BB reducedthe decrease of defect formation energy as more PDMS-BB were added. At aconstant loading of PDMS-BB, increasing the volume of PS-BB caused thedefect formation energy to decrease. It was observed that 3 vol % ofPS-BB can maintain the defect formation energies of blends of linearPS-b-PDMS diblock and both PS-BB and PDMS-BB to values greater than thedefect formation energy of pure linear diblock, >48 kT, over the entirerange of 1 to 9 vol % PDMS-BB. These data show that blends of linearPS-b-PDMS diblock and both PS-BB and PDMS-BB at certain compositionshave higher defect formation energies than pure linear diblockPS-b-PDMS. Table 2 shows defect formation energy for a linear PS-b-PDMSdiblock copolymer blended with various amounts of PS-BB and PDMS-BB in atrench with PDMS-block-attractive walls.

TABLE 2 PS-BB (vol %) 0 1 2 3 4 5 6 7 8 9 PDMS-BB 0 48 49 47 43 23 23 2222 22 21 (vol %) 1 63 59 52 50 50 50 50 46 45 44 2 64 61 59 54 55 52 5045 44 43 3 57 59 55 55 52 50 48 44 42 42 4 53 59 55 52 51 49 46 43 42 415 48 59 54 52 49 47 45 42 40 39 6 45 58 53 52 48 46 43 41 38 36 7 42 5854 49 46 44 42 41 38 35 8 39 57 51 48 45 43 43 42 42 40 9 38 57 53 53 4748 46 46 44 44

Example 8

This example describes the synthesis of apolystyrene-block-polymethyl-methacrylate block copolymer. Usingstandard Schlenk line methods, dry THF (421 mL) was transferred into adry, argon purged 1 L 3-neck round bottomed flask and cooled to −78° C.using a dry ice/acetone mixture. A 0.36M sec-butyllithium solution (2mL, 0.72 mmol) was added until a pale yellow color persisted. The flaskwas then warmed to room temperature and held at 30° C. until the colorcompletely disappeared (approximately 10-15 minutes). The THF solutionwas cooled back to −78° C. and styrene (25.11 g, 0.24 mol) wastransferred to the reaction flask via cannula. A 0.54M sec-Butyllithiuminitiator solution (0.81 mL, 0.44 mmol) was rapidly added to thereaction flask via syringe, causing a 17° C. exotherm within 1 minute.The reaction mixture cooled back down to −78° C. over the next 10minutes. The reaction was stirred for a total of 25 minutes and then asmall portion of reaction solution was transferred via cannula into asmall round bottomed flask containing anhydrous MeOH for GPC analysis ofthe PS block. Next, a diphenylethylene (0.10 g, 0.55 mmol) solution(diluted in 2.1 mL cyclohexane) was transferred to the THF/polystyrenesolution via cannula, causing the reaction mixture to turn from darkyellow to a dark ruby red. The solution was stirred for 10 minutes atapproximately −77° C. (measured by internal temperature probe). Next, amethyl methacrylate (10.57 g, 0.11 mol) solution (diluted with 11.0 mLcyclohexane) was transferred into the flask via cannula, which causedthe color to completely disappear. Following the MMA addition, thesolution warmed to approximately −68° C. within 2 minutes and thencooled back to −77° C. The reaction was stirred for a total of 130minutes, after which it was quenched by the addition of anhydrous MeOH.The block copolymer solution was precipitated into 1.4 L of methanol andcollected by vacuum filtration. The filter cake was then dissolved in150 mL of CH₂Cl₂ and washed twice with 100 mL of DI water. The blockcopolymer solution was precipitated into 1 L of methanol, collected byvacuum filtration and dried in a vacuum oven at 60° C. overnight.Analysis of the composition was completed by ¹H NMR spectroscopy and thefinal molecular weight was determined by GPC using a light scatteringdetector. Composition: 73.2 wt % PS, 26.8 wt % PMMA; Mn=66.9 kg/mol,PDI=1.07.

Example 9

This example describes the synthesis ofN-(hydroxyethyl)-cis-5-norbornene-endo(exo)-2,3-dicarboximide. A roundbottom flask was flame-dried and charged withcis-5-norbornene-endo(exo)-2,3-dicarboxylic anhydride (2.07 g, 1 eq.)and 2-aminoethanol (800 μL, 1.05 eq.). Toluene (20 mL) and triethylamine(200 μL, 0.11 eq.) were added to the flask, and the mixture was refluxedovernight using Dean-Stark trap. The mixture was then cooled down toroom temperature, concentrated using rotary evaporator, redissolved in40 mL dichloromethane and washed with brine and 0.1 M HCl. The organiclayer was dried by adding MgSO4 and concentrated to give the product asa white solid.

Example 10

This example describes the synthesis of the initiator for atom-transferradical polymerization (ATRP),2-(1,3-dioxo-3a,4,7,7a-tetrahydro-1H-4,7-methanoisoindol-2(3H)-yl)ethyl2-bromo-2-methyl-propanoate, shown above.N-(hydroxyethyl)-cis-5-norbornene-endo(exo)-2,3-dicarboximide (414.5 mg,1 eq.) was added into a flame-dried, 2 neck round bottom flask,dissolved in anhydrous dichloromethane (5 mL) and added withtriethylamine dropwise (1.2 eq.). The mixture was cooled in ice bath andα-bromo isobutyryl bromide (1.2 equiv) was added dropwise. Afterstirring for 20 hour the mixture was washed with brine and 0.1 M HCl,concentrated, and purified by column chromatography to obtain the ATRPinitiator as a white solid.

Example 11

This example describes the synthesis of the bottlebrush polymers withPMMA arms and polynorbornene backbone,poly(norbornene-g-polymethylmethacrylate).Dioxo-3a,4,7,7a-tetrahydro-1H-4,7-methanoisoindol-2(3H)-yl)ethyl2-bromo-2-methyl-propanoate was used as initiator to polymerize methylmethacrylate (MMA) according to the standard preparation of polymerusing ATRP with slight modification of the procedure described inGrimaud et al in Macromolecules 1997, 30, 2216-2218 using the followingratios of monomer, initiator, Cu(I)Br, andN,N,N′,N′,N″-pentamethyldiethylenetriamine (PMDETA) as ligand([MMA]:[initiator]:[Cu(I)]:[PMDETA]=100:1:0.5:0.5, 90° C.). After thereaction, copper was removed by passing the polymer solution through abasic alumina column, and the polymer was precipitated in cold methanolto obtain the norbornene PMMA macromonomer (PMMA-MM).

Ring-opening metathesis polymerization (ROMP) was then conducted on thePMMA macromonomer (PMMA-MM) (ca. 100 mg) by dissolving it in a minimumamount of degassed, anhydrous solvent ([PMMA-MM]=60-100 mM) andinjecting an appropriate amount of Grubbs 2^(nd) generation catalyst(1,3-Bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)dichloro(phenylmethylene)(tricyclohexylphosphine)ruthenium (40-55 mM, inanhydrous, deoxygenated solvent). The mixture was let stirred forovernight, precipitated in cold MeOH, filtered and dried for furtheranalysis. Three different PMMA bottlebrush polymer were made accordingto this technique, and their characteristics are collected in Table 3.

TABLE 3 Characterization of PMMA-BB polymers. Sample Mn (kg/mol) Mw/MnPMMA-BB-1  95 1.24 PMMA-BB-2 140 1.22 PMMA-BB-3 403, 190 1.23, 1.24(bimodal)

Comparative Example C

This example describes the formulation of a PS-b-PMMA linear blockcopolymer in solvent. A solution of PS-b-PMMA was prepared by dissolvingthe polymer (0.050 g) in toluene (4.95 g) to give a 1.0 wt % solution(polymer to total mass). The solution was filtered through a 0.2 μmTeflon filter.

Example 12

This example describes the formulation of a PS-b-PMMA linear blockcopolymer and a bottlebrush with PMMA arms and polynorbornene backbone(PMMA-BB-1) in solvent in various ratios. PS-b-PMMA and PMMA-BB-1 atvarious ratios were dissolved in toluene to give 1.0 wt % solutions(polymer to total mass). The solutions were filtered through 0.2 μmTeflon filters. Table 4 shows formulation details.

TABLE 4 Polymer Polymer Block Bottle Brush Conc. Example Comp. CopolymerPolymer Solvent (wt %) Comp C. PC -1 PS-b-PMMA NA Toluene 1.0 (0.050 g)(4.950 g) 12a PC-2 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.048 g) (0.003 g)(4.950 g) 12b PC-3 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.045 g) (0.005 g)(4.950 g) 12c PC-4 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.040 g) (0.010 g)(4.950 g) 12d PC-5 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.048 g) (0.003 g)(4.950 g) 12b PC-6 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.045 g) (0.005 g)(4.950 g) 12e PC-7 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.040 g) (0.010 g)(4.95 g) 12f PC-8 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.048 g) (0.003 g)(4.950 g) 12g PC-9 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.045 g) (0.005 g)(4.950 g) 12h PC-10 PS-b-PMMA PMMA-BB-1 Toluene 1.0 (0.040 g) (0.010 g)(4.950 g)

Comparative Example A

This example demonstrates behavior of a PS-b-PMMA linear block copolymerdisposed as a thin film on a silicon substrate and annealed. Ahydroxyl-terminated poly(styrene-r-methylmethacrylate) bush (preparedaccording to the method described by Han et al. in Macromolecules, Vol.41, No. 23, 2008, p. 9090-9097, with 75 mol % styrene, Mn=10 kg/mol, andMw/Mn=1.2), was dissolved in toluene to a give 1 wt % solution andfiltered through a 0.2 μm Teflon filter. The surface of a siliconsubstrate having a native oxide layer was then modified by spin coatingthereon this brush solution at 1,500 rpm for 30 sec. The substrate wasthen placed on a hotplate set at 120° C. for 2 minutes and then 220° C.for 60 minutes to anneal the deposited brush layer. The substrate wasthen rinsed with PGMEA to wash away any unattached polymer by firstsoaking the substrate in PGMEA for 30 s and then spin drying at 3,000rpm for 1 minute. The substrate was then baked on a hotplate set at 130°C. for 60 seconds. Thin films were prepared of the PS-b-PMMA formulationdescribed in Comparative Example C by spin coating the solution on theP(S-r-MMA)-OH brushed silicon wafer. The formulation was spin-coated at2000 rpm onto a brushed substrate, baked on a hot plate at 130° C. for 1minute, and annealed at 240° C. for 5 minutes under nitrogen. Afterthermal annealing, the films were subjected to reactive ion etchingusing a PlasmaTherm 790i RIE, a 8 second CHF₃ reactive ion etch followedby a 15 second oxygen reactive ion etch to remove the PMMA. The sampleswere then imaged by scanning electron microscopy (Hitachi CG4000) at40,000× and 400,000× magnification to characterize the morphology.

Example 13

This example demonstrates behavior of blends of a PS-b-PMMA linear blockcopolymer with a bottlebrush with PMMA arms and polynorbornene backbone(PMMA-BB) disposed as a thin film on a silicon substrate and annealed. Ahydroxyl-terminated poly(styrene-r-methylmethacrylate) bush (preparedaccording to the method described by Han et al. in Macromolecules, Vol.41, No. 23, 2008, p. 9090-9097, with 75 mol % styrene, Mn=10 kg/mol, andMw/Mn=1.2), was dissolved in toluene to a give a 1 wt % solution andfiltered through a 0.2 μm Teflon filter. The surface of a siliconsubstrate having a native oxide layer was then modified by spin coatingthereon this brush solution at 1,500 rpm for 30 sec. The substrate wasthen placed on a hotplate set at 120° C. for 2 minutes and then 220° C.for 60 minutes to anneal the deposited brush layer. The substrate wasthen rinsed with PGMEA to wash away any unattached polymer by firstsoaking the substrate in PGMEA for 30 s and then spin drying at 3,000rpm for 1 minute. The substrate was then baked on a hotplate set at 130°C. for 60 seconds. The substrate was diced into small pieces for furtherexperiments. Thin films were then prepared of the PS-b-PMMA formulationsdescribed in Example 12 by spin coating the solution on theP(S-r-MMA)-OH brushed silicon wafer. The formulation was spin-coated at2000 rpm onto a brushed substrate, baked on a hot plate at 130° C. for 1minute, and annealed at 240° C. for 5 minutes under nitrogen. Afterthermal annealing, the films were subjected to reactive ion etchingusing a PlasmaTherm 790i RIE, a 8 second CHF₃ reactive ion etch followedby a 15 second oxygen reactive ion etch to remove the PMMA. The sampleswere then imaged by scanning electron microscopy (Hitachi CG4000) at40,000× and 400,000× magnification to characterize the morphology.

Example 14

This example describes synthesis of hydroxyl-terminated polystyrenebrushes. Hydroxyl-terminated polystyrene brushes (PS-OH-1 and PS-OH-2)were prepared according to the following procedure, where the monomer toinitiator ratio was adjusted to vary the molecular weight. Styrene and2-hydroxyethyl 2-bromo-2-methylpropanoate (initiator) were dissolved inanisole in a 500 mL round bottom flask. CuBr (0.1 equivalent relative toinitiator) and tris[2-(dimethylamino) ethyl] amine (0.1 equivalentrelative to initiator) were dissolved in 5 mL anisole in a sample vial.Sn(EH)₂ (0.1 equivalent relative to initiator) was dissolved in 5 mLanisole in a sample vial. The three solutions were purged with nitrogenfor 1 hour and then combined in the 500 mL flask. The mixture was thenheated for 20 h, and the polymer was then precipitated into methanol.The precipitate was then dissolved in THF and treated with an ionexchange resin to remove the Cu catalyst. The reaction mixture was thenre-precipitated into methanol. The resulting white powder was filteredand dried overnight at 50° C. Two materials were synthesized, PS-OH-1with Mn=8.8 kg/mol, and Mw/Mn=1.23, and PS-OH-2 with Mn=37.3 kg/mol, andMw/Mn=1.23.

Example 15

This example describes synthesis of linearpolystyrene-block-polydimethyl-siloxane (PS-b-PDMS) block copolymers.Three linear PS-b-PDMS block copolymers were prepared according to theprocedure outlined by Hustad et al. in U.S. Pat. No. 8,821,738. Detailsof the polymer characterization are given in Table 5.

TABLE 5 Sample Mn (kg/mol) Mw/Mn PDMS (wt %) PDMS (vol %) PS-b-PDMS-2639.6 1.09 24.7 26.2 PS-b-PDMS-29 40.3 1.07 27.4 29.0 PS-b-PDMS-31 39.61.08 29.2 30.9

Example 16

This example describes the synthesis of a bottlebrush polymer withpolydimethylsiloxane (PDMS) arms and polynorbornene backbone,poly(norbornene-g-polydimethylsiloxane) (PDMS-BB).2-(Prop-2-yn-1-yl)-3a,4,7,7a-tetrahydro-1H-4,7-methanoisoindole-1,3(2H)-dionewas synthesized according to the procedure described in Macromolecules2010, 43, 5611-5617. Azide terminated PDMS was synthesized according toliterature (J Polym Sci Pol Chem 2014, 52, 3372-3382). A flame-dried 20mL vial was charged with a stirrer bar,2-(Prop-2-yn-1-yl)-3a,4,7,7a-tetrahydro-1H-4,7-methanoisoindole-1,3(2H)-dione(3.2 mg) and the azide terminated PDMS (0.174 g, 1 eq.). Degassed,anhydrous tetrahydrofuran (THF) (2 mL) was added into the flask, and 0.3mL of a Cu stock solution (prepared from 1 mg Cu(I)Br and 5 μL PMDETA in1 mL anhydrous THF). The reaction mixture was stirred and heated at 50°C. overnight. Cu was removed from the macromonomer solution by passingthrough basic alumina, and the polymer solution was then concentratedand precipitated in cold MeOH. Ring-opening metathesis polymerization(ROMP) was then conducted on the PDMS macromonomer (PDMS-MM) (ca. 100mg) by dissolving it in a minimum amount of degassed, anhydrous solvent([PDMS-MM]=60-100 mM) and injecting an appropriate amount of Grubbs3^(nd) generation catalyst,(1,3-Bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)dichloro(phenyl-methylene)(dipyridine)ruthenium(55 mM, [PDMS-MM]/[catalyst]=30, in anhydrous, deoxygenated solvent).The mixture was let stirred for overnight, precipitated in cold MeOH,filtered and dried for further analysis. GPC of the isolated polymershowed a multimodal trace that was deconvoluted into the followingcomponents: Peak 1, Mn=230 kg/mol, Mw/Mn=1.51; Peak 2: 78 kg/mol,Mw/Mn=1.46; Peak 3: 9 kg/mol, Mw/Mn=1.5 (corresponding to the PDMS-MM).

Comparative Example E

This example describes the formulation of a PS-b-PDMS linear blockcopolymers in solvent. Solutions of PS-b-PDMS-26, PS-b-PDMS-29, andPS-b-PDMS-31 were prepared by dissolving the polymers in 50/50 volumepercent mixtures of propylene glycol monomethyl ether acetate (PGMEA)and n-butylacetate (NBA) at 1.2 wt % polymer to total mass. Thesolutions were filtered through a 0.2 μm PTFE filters.

Example 17

This example describes the formulation of PS-b-PDMS-26 with thebottlebrush with PDMS arms and polynorbornene backbone (PDMS-BB) insolvent. A solution of PDMS-BB was prepared by dissolving the polymer ina 50/50 volume percent mixture of propylene glycol monomethyl etheracetate (PGMEA) and n-butylacetate (NBA) at 1.2 wt % polymer to totalmass. This solution was blended in different ratios with the solution ofPS-b-PDMS-26 to give formulations with different ratios of PDMS-BB toPS-b-PDMS. The solutions were filtered through 0.2 μm PTFE filters. Thedifferent formulations are listed in Table 6.

TABLE 6 Minority PS-b-PDMS PDMS-BB composition Sample (vol %) (vol %)(vol %) Comparative 100 0 26.2 Example E Example 17a 97.5 2.5 28.0Example 17b 95 5.0 29.9 Example 17c 92.5 7.5 31.7 Example 17d 90 10 33.6Example 17e 80 20 41.0 Example 17f 70 30 48.3

Example 18

This example describes preparation of silicon wafer substrates to becoated with thin films of the formulations. The hydroxyl-terminatedpolystyrene bushes, PS-OH-1 and PS-OH-2, prepared according to Example14 were individually dissolved in propylene glycol monomethyl etheracetate (PGMEA) to give 1.5 wt % solutions. The solutions were thenblended in a 50/50 volume ratio to give a final brush formulation, whichwas filtered through a 0.2 μm Teflon filter. The surface of a siliconsubstrate having a native oxide layer was then modified by spin coatingthereon this brush solution at 1,500 rpm for 30 seconds. The substratewas then placed on a hotplate set at 250° C. for 2 minutes to anneal thedeposited brush layer. The substrate was then rinsed with PGMEA to washaway any unattached polymer by first soaking the substrate in PGMEA for30 s and then spin drying at 3,000 rpm for 1 minute. The substrate wasthen baked on a hotplate set at 130° C. for 60 seconds.

Comparative Example F

This example describes thin film formation of linear PS-b-PDMS on thePS-OH brushed substrate. Thin films were prepared of the PS-b-PDMSformulations described in Comparative Example E by spin coating thesolutions on PS-brushed silicon wafers prepared in Example 18. Theformulations were spin-coated at 1,200 rpm onto a brushed substrate,baked on a hot plate at 130° C. for 1 minute, and annealed at 340° C.for 2 minutes under nitrogen. After thermal annealing, the films weresubjected to two reactive ion etching steps using a PlasmaTherm 790iRIE, a 4 second CF₄ reactive ion etch (50 standard cubic centimeters(sccm), 100 watts) followed by a 8 second oxygen reactive ion etch (25sccm, 180 watts) to remove the PS and oxidize the PDMS block. Thesamples were then imaged by scanning electron microscopy (HitachiCG4000) at 40,000× and 400,000× magnification to characterize themorphology. The morphology for comparative examples D, E and F is shownin a photomicrograph in FIG. 11. The formulation with 26 vol % revealsthe expected “fingerprint” structure from the oxidized PDMS cylinders.However, as the PDMS volume percent increase, the desired thefingerprint pattern largely disappears. These formulations at higherPDMS loadings are therefore not useful for forming nanoscale linepatterns.

Example 19

This example describes thin film formation of blends of linear PS-b-PDMSwith PDMS bottlebrush polymers (PDMS-BB) on PS-OH brushed substrates.Thin films were prepared of the formulations described in Example 17 byspin coating the solutions on the PS-brushed silicon wafers prepared inExample 18. The formulations were independently spin-coated at 1,200 rpmonto brushed substrates, baked on a hot plate at 130° C. for 1 minute,and annealed at 340° C. for 2 minutes under nitrogen. After thermalannealing, the films were subjected to two reactive ion etching stepsusing a PlasmaTherm 790i RIE, a 4 second CF₄ reactive ion etch (50standard cubic centimeters (sccm), 100 watts) followed by a 8 secondoxygen reactive ion etch (25 sccm, 180 watts) to remove the PS andoxidize the PDMS block. The samples were then imaged by scanningelectron microscopy (Hitachi CG4000) at 40,000× and 400,000×magnification to characterize the morphology. The morphologies are shownin the photomicrographs of FIG. 12. Unlike the thin films in ComparativeExample F, the micrographs all reveal “fingerprint” structures from theoxidized PDMS cylinders, even in formulations with very high PDMS volumepercentages.

What is claimed is:
 1. A composition comprising: a block copolymer;where the block copolymer comprises a first polymer and a secondpolymer; where the first polymer and the second polymer of the blockcopolymer are different from each other and the block copolymer forms aphase separated structure; an additive polymer; where the additivepolymer comprises a bottlebrush polymer; and where the bottlebrushpolymer comprises a polymer that is chemically and structurally the sameas one of the polymers in the block copolymer or where the bottlebrushpolymer comprises a polymer that has a preferential interaction with oneof the blocks of the block copolymers; and a solvent.
 2. The compositionof claim 1, where the bottlebrush polymer comprises a third polymer;where the third polymer is chemically identical with or substantiallychemically similar to either the first polymer or the second polymer ofthe block copolymer; or where the bottlebrush polymer is a copolymerthat comprises a third polymer and a fourth polymer; where the thirdpolymer and the fourth polymer of the bottlebrush copolymer aredifferent from each other; where the first polymer of the blockcopolymer is chemically identical with or substantially chemicallysimilar to the third polymer of the bottlebrush copolymer or where thesecond polymer of the block copolymer is chemically identical with orsubstantially chemically similar to the fourth polymer of thebottlebrush copolymer.
 3. The composition of claim 1, where the firstpolymer is a vinyl aromatic polymer obtained by a polymerization ofunits having a structure of formula (1):

wherein R⁵ is hydrogen, an alkyl, a haloalkyl or halogen; Z¹ ishydrogen, halogen, a hydroxyl, a haloalkyl or an alkyl; and p is from 1to
 5. 4. The composition of claim 1, where the second polymer isobtained from a polymerization of units having a structure representedby formula (2):

where R₁ is a hydrogen or an alkyl group having 1 to 10 carbon atoms, orwhere the second polymer has a structure derived from a monomer having astructure represented by the formula (3):

where R₁ is a hydrogen or an alkyl group having 1 to 10 carbon atoms andR₂ is a C₁₋₁₀ alkyl, a C₃₋₁₀ cycloalkyl, or a C₇₋₁₀ aralkyl group. 5.The composition of claim 1, where the bottlebrush copolymer is apoly(norbornene-g-polymethylemthacrylate) or apoly(norbornene-g-polystyrene) or apoly(norbornene-g-polymethylmethacrylate-g-polystyrene).
 6. Thecomposition of claim 1, where the block copolymer comprises polystyreneand polymethylmethacrylate and where the polymethylmethacrylate ispresent in an amount of 20 to 35 volume percent based on a total volumeof the block copolymer.
 7. The composition of claim 1, where the blockcopolymer is present in an amount of 85 to 99 wt %, based on a totalweight of the block copolymer and the additive polymer and where theadditive polymer is present in an amount of 1 to 15 wt %, based on atotal weight of the block copolymer and the additive polymer.
 8. Thecomposition of claim 1, where the second polymer is an α-alkyl acrylate,methacrylate, ethacrylate, propyl acrylate, butyl acrylate, or acombination comprising at least one of the foregoing acrylates.